Any type of food is off-limits, no matter how soft it may be. The same is true of any leftover pieces, shells, bones or grounds that you want to get rid of. These belong in neither your pipes nor your garbage disposal. Throw them in the garbage bin or compost.
Water does nothing to get rid of gum, so it tends to stick around – literally. You don’t want that in your pipes!
If you’re fishing hairballs from your sink or tub, don’t dump them in the toilet: That’s just moving the clog from one part of your plumbing to another. Throw it away instead.